Grisanov Theorem in Finance: All You Need to Know
The Whispering Void What is Grisanov Theorem? Girsanov theorem explains how to shift measurement from the real world to the risk-neutral universe. We can transition from one Brownian motion to another by using…
Risk Neutral Valuation in Finance: All You Need to Know
What is Risk Neutral Valuation? Risk neutral valuation involves valuing options based on their expected payoffs, discounted from expiration to present, with the assumption of average growth at the risk-free…
Ito Lemma in Finance: All You Need to Know
What is Ito Lemma? Ito lemma is a theorem in stochastic calculus. This means that if you have a random walk in y and a function called f (y, t),…
Jensen Inequality in Finance: All You Need to Know
What is Jensen Inequality? Jensen Inequality states that if f(.) is a convex function and x is a random variable, then This explains why non-linear instruments and options have inherent…
Brownian Motion in Finance: All You Need to Know
What is Brownian Motion? Brownian Motion is a stochastic process with stationary independent, normally distributed increments and continuous sample pathways. This is the most commonly used stochastic building component for…
Utility Function in Finance: All You Need to Know
What is Utility Function? A utility function evaluates the value, happiness, or satisfaction of commodities, services, events, outcomes, and wealth levels. It can rate results, aggregate ‘pleasure’ among individuals, and…
Most Useful Performance Measures in Finance: All You Need to Know
What are Performance Measures? Performance measures quantify the outcome of a trading strategy. In most cases, they are risk adjusted. The Sharpe ratio is the most popular. A Short Example…
Efficient Markets Hypothesis in Finance: All You Need to Know
What is Efficient Markets Hypothesis? In an efficient markets, securities prices already reflect all relevant information, making it impossible to beat the market. A Short Example A counter-example: “I’d be…
Marking To Market and its impact on Risk in Trading: All You Need to Know
What is Marking to Market? Marking to market involves valuing an instrument based on its current market price. If you buy an option because you believe it is cheap, the…
Hedging in Quantitative Finance: All You Need to Know
What is Hedging? In its broadest definition, ‘hedging’ involves reducing risk by leveraging correlations or lack thereof between hazardous investments. Hedging aims to optimise risk/return ratios. The standard Modern Portfolio…